Megaminx First Two Layers or Megaminx F2L (not to be confused with 3x3x3 F2L) refers to solving the first two layers of a Megaminx, usually followed by S2L. Basically all Megaminx solvers start the solve this way.
There are two main approaches to Megaminx F2L:
Star and Pairs
Like in the popular 3x3x3 method CFOP, the solver starts by solving all edges of one side and then finishing the first two layers by creating and inserting pairs. As five edges need to be solved on the Megaminx compared to only four on 3x3x3, CFOP's Cross step is referred to as the "Star" on Megaminx because of the star-like shape. After that, the solver connects a corner of the first layer with its corresponding edge to form a pair. This pair is inserted into its respective slot and this process is done five times in total to solve all pieces of the first two layers.
While high tps can be reached here, this is not the most efficient way to solve the F2L.
Blockbuilding is more of a freestyle approach to Megaminx F2L. Instead of forming F2L pairs, the solver chooses any pair of F2L pieces (including star edge - corner and center - edge pairs) which can be solved efficiently, i.e. in the smallest amount of moves. This approach is similar to that of the Petrus method for 3x3x3.
While this is certainly the most efficient approach, tps is usually lower because more thinking is required.